The US-drafted resolution declared there was a "need to pursue further efforts in the sphere of nuclear disarmament"."
It also urged all countries that have not signed the 1970 Non-Proliferation Treaty (NPT) to do so.
Al Jazeera's Mike Hannah, reporting from New York, said: "The backdrop to these ongoing discussions about nuclear disarmament and non-proliferation is how one divides those that are allowed to have nuclear weapons, from those that are not.
"For example, we have repeated criticism of Iran's enriched uranium programme [but] there is very seldom ... any criticism of Israel's ongoing enrichment programme
"Israel has constantly refused to allow any access or examination of either its capability or stockpile - the very point at which Iran has been refusing to do.
"Iran has received international criticism, while Israel has not from those who criticise Iran.
"This is just an example of why the issue makes the situation complex."
'Wave of disarmament'
The meeting of the 15-member body in New York was the first-ever chaired by a US president since the council was established in 1946.
Hans Blix, the former director of the International Atomic Energy Agency (IAEA), told Al Jazeera: "These proceedings ... are very important to start a wave of disarmament.
"President Obama has changed the situation very much and we are looking forward to a conference on non-proliferation treaty next spring and I think he wants to set the table right for that.
"I think this is the first occasion when there is a chance for diplomatic talks.
"Iranians ... have said they want to talk about reform of the Security Council, about settlements in the Middle East etc, while the other side wants to talk about the enrichment programme.
"Nevertheless, there will now be a chance for them to exchange views and see if there is anyway in which they can agree."
All five permanent Security Council members - the United States, Russia, China, Britain and France - have nuclear weapons.
NPT signatories without nuclear capabilities have criticised the permanent council members for barring other nations from developing nuclear programmes while failing to live up to commitments to disarm.
Mark Fitzpatrick, the director of the non-proliferation programme at the International Institute for Strategic Studies, told Al Jazeera: "All but three or four of the nations of the world have committed themselves to not pursuing nuclear weapons by signing the non-proliferation treaty.
"All those who had nuclear weapons at the time of treaty are allowed to have them and those five are committed to negotiating in good faith to limit the weapons."
Obama held bilateral talks with Dmitry Medvedev, his Russian counterpart, on Wednesday at which they spoke about plans for an agreement to replace the Strategic Arms Reduction Treaty (Start) nuclear arms reduction treaty.
"Both of us are confident that we can meet our self-imposed deadline" to reach an agreement to reduce the number of nuclear missiles and launchers "by the end of the year," Obama said after the talks.
Medvedev also suggested that Moscow was moving closer to backing fresh sanctions against Iran, saying that while such tactics were rarely productive, "in some cases sanctions are inevitable".
"Our task is to maintain a system of incentives allowing Iran to use peaceful nuclear energy but [we] will not allow the creation of nuclear weapons," he said.
Iran has refused to suspend its uranium enrichment activities, as demanded by the UN Security Council, and denies its nuclear programme is aimed at producing an atomic weapon.
A draft of the resolution did not name Iran nor North Korea, which has carried out nuclear tests in defiance of the NPT, but refered to "current major challenges to the non-proliferation regime".